How fast can we burn, 2.0

We review the state of the art in measurements and simulations of the behavior of premixed laminar and turbulent flames, subject to differential diffusion, stretch and curvature. The first part of the paper reviews the behavior of premixed laminar flames subject to flow stretch, and how it affects the accuracy of measurements of unstrained laminar flame speeds in stretched and spherically propagating flames. We then examine how flow field stretch and differential diffusion interact with flame propagation, promoting or suppressing the onset of thermodiffusive instabilities. Secondly, we survey the methodology for and results of measurements of turbulent flame speeds in the light of theory, and identify issues of consistency in the definition of mean flame speeds, and their corresponding mean areas. Data for methane at a single operating condition are compared for a range of turbulent conditions, showing that fundamental issues that have yet to be resolved for Bunsen and spherically propagating flames. Finally, we consider how the laminar flame scale response of flames to flow perturbations interacting with differential diffusion leads to very different outcomes to the overall sensitivity of the burning rate to turbulence, according to numerical simulations (DNS). The paper concludes with opportunities for future measurements and model development, including the perennial recommendation for robust archival databases of experimental and DNS results for future testing of models.     

Exploring fuel isomeric effects on laminar flame propagation of butylbenzenes at various pressures

This work reports an experimental and kinetic modeling investigation on the laminar flame propagation of three butylbenzene isomers (n-butylbenzene, iso-butylbenzene and tert-butylbenzene)/air mixtures. The experiments were performed in a high-pressure constant-volume cylindrical combustion vessel at the initial temperature of 423 K, initial pressures of 1–10 atm, and equivalence ratios (?) of 0.7–1.5. The laminar burning velocities of butylbenzene/O₂/He mixtures were also measured at 423 K, 10 atm and ? = 1.5 to provide additional experimental data under conditions that the butylbenzene/air experiments are susceptible of cellular instability. Comparison among the laminar burning velocities of butylbenzenes including both the three isomers investigated in this work and sec-butylbenzene investigated in our recent work [Combust. Flame 211 (2020) 18–31] shows remarkable fuel isomeric effects, that is, iso-butylbenzene has the slowest laminar burning velocities, followed by n-butylbenzene and tert-butylbenzene, while sec-butylbenzene has the fastest laminar burning velocities. A kinetic model for butylbenzene combustion was developed to simulate the laminar flame propagation of butylbenzenes. Sensitivity analysis was performed to reveal important reactions in laminar flame propagation of butylbenzenes, including both small species reactions and fuel-specific reactions. Kinetic effects are concluded to result in the different laminar burning velocities of four butylbenzene isomers. Small species reactions control the laminar flame propagation under lean conditions, which results in small differences of laminar burning velocities. Chain termination reactions, especially fuel-specific reactions, have important contributions to inhibit the laminar flame propagation under rich conditions. The structural features of butylbenzene isomers can significantly affect the formation of some crucial radicals such as methyl, cyclopentadienyl and benzyl radicals under rich conditions, which leads to remarkable fuel isomeric effects on their laminar burning velocities, especially at high pressures.     

Measurement of unstable burning velocities of iso-octane–air mixtures at high pressure and the derivation of laminar burning velocities

A new technique is reported for measuring burning velocities at high pressures in the final stages of two inwardly propagating flame kernels in an explosion bomb. The flames were initiated at diametrically opposite spark electrodes, close to the wall, in quiescent mixtures. Measurements of pressure and flame kernel propagation speeds by high-speed photography showed the burning velocities to be elevated above the corresponding laminar burning velocities as a result of the developing flame instabilities. The enhancement increased with increase in pressure and decreased with increase in Markstein number. When the Markstein number was negative, instabilities could be appreciable, as could the enhancement. For the iso-octane–air mixtures investigated, where the mixtures had well-characterised Markstein numbers or critical Peclet numbers at the relevant pressures and temperatures, it was possible to explain the enhancement quantitatively by the spherical explosion flame instability theory of Bechtold and Matalon, provided the critical Peclet number was that observed experimentally, and allowance was made for the changing pressure. With this theoretical procedure, it was possible to derive values of laminar burning velocity from the measured values of burning velocity over a wide range of equivalence ratios, pressures, and temperatures. The values became less reliable at the higher temperatures and pressures as the data on Markstein and critical Peclet numbers became less certain. It was found that with iso-octane as the fuel the laminar burning velocity decreased during isentropic compression.     

Turbulent flame speed and morphology of pure ammonia flames and blends with methane or hydrogen

Ammonia appears a promising hydrogen-energy carrier as well as a carbon-free fuel. However, there remain limited studies for ammonia combustion especially under turbulent conditions. To that end, using the spherically expanding flame configuration, the turbulent flame speeds of stoichiometric ammonia/air, ammonia/methane and ammonia/hydrogen were examined. The composition of blends studied are currently being investigated for gas turbine application and are evaluated at various turbulent intensities, covering different kinds of turbulent combustion regimes. Mie-scattering tomography was employed facilitating flame structure analysis. Results show that the flame propagation speed of ammonia/air increases exponentially with increasing hydrogen amount. It is less pronounced with increasing methane addition, analogous to the behavior displayed in the laminar regime. The turbulent to laminar flame speed ratio increases with turbulence intensity. However, smallest gains were observed at highest hydrogen content, presumably due to differences in the combustion regime, with the mixture located within the corrugated flamelet zone, with all other mixtures positioned within the thin reaction zone. A good correlation of the turbulent velocity based on the Karlovitz and Damköhler numbers is observable with the present dataset, as well as previous experimental measurements available in literature, suggesting that ammonia-based fuels may potentially be described following the usual turbulent combustion models. Flame morphology and stretch sensitivity analysis were conducted, revealing that flame curvature remains relatively similar for pure ammonia and ammonia-based mixtures. The wrinkling ratio is found to increase with both increasing ammonia fraction and turbulent intensity, in good agreement with measured increases in turbulent flame speed. On the other hand, in most cases, the flame stretch effect does not change significantly with increasing turbulence, whilst following a similar trend to that of the laminar Markstein length.     

Insight into fuel isomeric effects on laminar flame propagation of pentanones

Laminar flame propagation was investigated for pentanone isomers/air mixtures (3-pentanone, 2-pentanone and 3-methyl-2-butanone) in a high-pressure constant-volume cylindrical combustion vessel at 393–423 K, 1–10 atm and equivalence ratios of 0.6–1.5, and in a heat flux burner at 393 K, 1 atm and equivalence ratios of 0.6–1.5. Two kinds of methods generally show good agreement, both of which indicate that the laminar burning velocity increases in the order of 3-methyl-2-butanone, 2-pentanone and 3-pentanone. A kinetic model of pentanone isomers was developed and validated against experimental data in this work and in literature. Modeling analysis was performed to provide insight into the flame chemistry of the three pentanone isomers. H-abstraction reactions are concluded to dominate fuel consumption, and further decomposition of fuel radicals eventually produces fuel-specific small radicals. The differences in radical pools are concluded to be responsible for the observed fuel isomeric effects on laminar burning velocity. Among the three pentanone isomers, 3-pentanone tends to produce ethyl and does not prefer to produce methyl and allyl in flames, thus it has the highest reactivity and fastest laminar flame propagation. On the contrary, 3-methyl-2-butanone tends to produce allyl and methyl instead of ethyl, and consequently has the lowest reactivity and slowest laminar flame propagation.     

Methane flames in a jet impinging onto a wall

Traditionally, research has focused on positive stretch in the stagnation flow and negative stretch along the Bunsen flame. Only a very limited amount of research has been devoted to studying the behavior of a conical Bunsen flame established in a stagnation flow, which is significantly affected by the combined effects of the curvature stretch and the aerodynamic straining. This investigation is aimed at studying the characteristics of laminar conical premixed flames in an impinging jet flow experimentally and theoretically. First, we analyze the transport processes of a nonreactive impinging jet flow numerically. For lower burner-to-plate distance, the potential core becomes concave at the top. Hence, a conical Bunsen flame established in such a flow field may suffer positive flow stretch. The predicted flame shapes using a simple model incorporated with the numerical results agree well with the experimental observations. Flame shapes exhibit double-solution characteristics in a certain range of methane concentrations. Experimentally, by following different paths of adjusting methane concentration (decreasing from rich to lean or increasing from lean to rich), two different flame configurations (planar or conical flame) may exist at the same flow conditions, namely burner-to-plate distance, inlet velocity, and methane concentration. At the higher (or lower) critical methane concentration, the transition from a flat flame to a conical flame (or from a conical flame to a flat flame) occurs. The calculation of stretch and measurement of flame temperature for the low inlet velocity, 0.8 m/s, show that the stretch of a conical flame established in a stagnation flow is negative (dominated by the flame curvature). However, it is important to emphasize that at high velocity, e.g., U_in = 1.6 m/s, a negatively stretched flame tip can suffer positive flow stretch. This significant finding has been verified in the experiment since the conical flame tip is higher than the positively stretched flat flame.     

Evaluation of models for flame stretch due to curvature in the thin reaction zones regime

Direct numerical simulation (DNS) was used to study modelling assumptions for the curvature-propagation component of flame stretch in the thin reaction zones regime of turbulent premixed combustion, a regime in which small eddies can penetrate the preheat zone but not the thinner fuel breakdown zone. Simulations of lean hydrogen–air and methane–air flames were conducted, and statistics of flame stretch due to curvature, henceforth referred to simply as stretch, were extracted from a species mass fraction iso-surface taken to represent the flame. The study focussed on investigating the modelling assumptions of Peters [J. Fluid Mech. 384 (1999) 107]. It was found that the mean stretch is dominated by stretch due to correlations of flame speed with curvature, and specifically the effects of tangential diffusion. The modelling suggestions of Peters were found to provide an improvement over the assumptions of a constant flame speed or a flame speed governed by the linear relationship with stretch at small and steady stretch. However for the conditions considered here, diffusive-thermal effects remain well into the thin reaction zones regime, and the suggestions of Peters generally over-predict the mean compressive stretch. An effective diffusivity for flame stretch was suggested and evaluated for the methane simulations. It was found that the effective diffusivity was comparable to the mass diffusivity for flames with a high ratio of flame time to eddy turnover time. The length scales contributing to stretch were investigated, and it was found that while most flame area has a radius of curvature greater than the laminar flame thickness, most stretch occurs in more tightly curved flame elements.     

双组分燃料的层流火焰速度模型

以往关于层流火焰速度的理论分析均只考虑单组分燃料,本文对双组分燃料的平面火焰进行了大活化能渐近理论分析。在理论分析中,将火焰结构分为预热区、化学反应区和平衡区,并在大活化能假设下对各个区域分别求解了关于温度与燃料质量分数的微分方程。根据每两个区域分界面上满足的结合条件,本文推导出了双组分燃料的层流火焰速度模型。该模型表明双组分燃料层流火焰速度的平方为各个单组分燃料层流火焰速度平方的加权平均。     

On the laminar flame propagation of C5H10O2 esters up to 10 atm: A comparative experimental and kinetic modeling study

Biodiesel is a family of renewable engine fuels with carbon-neutral nature. In this work, three C₅H₁₀O₂ esters (methyl butanoate, methyl isobutanoate and ethyl propanoate), which can serve as model compounds of biodiesel and represent linear and branched methyl esters and linear ethyl esters, were investigated to characterize their laminar flame propagation characteristics up to 10 atm and unravel the effects of isomeric fuel structures. A high-pressure constant-volume cylindrical combustion vessel was used to achieve laminar burning velocity measurements at 1–10 atm, 423 K and equivalence ratios of 0.7–1.5, while comparative experimental work was performed on a heat flux burner at 1 atm, 393 K and equivalence ratios of 0.7–1.6 for methyl butanoate and ethyl propanoate. The laminar burning velocity generally decreases with increasing pressure and increases in the order of methyl isobutanoate, methyl butanoate and ethyl propanoate, which shows distinct fuel isomeric effects. A kinetic model of C₅H₁₀O₂ esters was developed and validated against the new data in this work and previous data in literature. Modeling analyses were performed to provide insight into the fuel-specific flame chemistry of the three esters isomers. Remarkable differences in radical pools of three ester isomers are concluded to be responsible for the observed fuel isomeric effects on laminar flame propagation. The feature of two ethyl groups connected to the ester group in ethyl propanoate facilitates the ethyl production and inhibits the methyl and allyl production, making it propagate fastest among the three isomers. The branched structure feature of methyl isobutanoate with methyl and i-propyl groups connected to the ester group prevents the ethyl formation and results in considerable CH₃ and allyl production, which decelerates its laminar flame propagation.     

Parameters influencing the burning rate of laminar flames propagating into a reacting mixture

The laminar flame speed is an important property of a reacting mixture and it is used extensively for the characterization of the combustion process in practical devices. However, under engine-relevant conditions, considerable reactivity may be present in the unburned mixture, introducing thus challenges due to couplings of auto-ignition and flame propagation phenomena. In this study, the propagation of transient, one-dimensional laminar flames into a reacting unburned mixture was investigated numerically in order to identify the parameters influencing the flame burning rate in the conduction-reaction controlled regime at constant pressure. It was found that the fuel chemical classification significantly influences the burning rate. More specifically, for hydrogen flames, the “evolution” of the burning rate does not depend on the initial unburned mixture temperature. On the other hand, for n-heptane flames that exhibit low temperature chemistry, the burning rate depends on the instantaneous temperature and composition of the unburned mixture in a coupled way. A new approach was developed allowing for the decoupling the flame chemistry from the ignition dynamics as well as for the decoupling of parameters influencing the burning rate, so that meaningful sensitivity analysis could be performed. It was determined that the burning rate is not directly affected by fuel specific reactions even in the presence of low temperature chemistry whose effect is indirect through the modification of the reactants composition entering the flame. The controlling parameters include but not limited to mixture conductivity, enthalpy, and the species composition evolution in the unburned mixture.     

Unsteady propagation of premixed methane/propane flames in a mesoscale disk burner of variable-gaps

Unsteady flame propagation of air-premixed methane and propane flames was investigated in a new mesoscale disk burner, of which disk-gap could be precisely varied. To begin with, the quenching disk-gaps on the flammability limits were measured. In most cases, with the slight increase of the disk-gap, cellular flame structures could be generated. The initiation of such cellular structures could be explained by the thermally induced hydrodynamic instability, and it could be enhanced if the Lewis number was sufficiently small. When the disk-gap was sufficiently larger than a critical value (approximately 1.5 times the quenching distance), the cellular flame structure changed into a smooth one in the azimuthal direction. With a further increase of the disk-gap, the flame propagation velocities approached to constant values. These values were comparable to the laminar burning velocities except for the propane-rich conditions, in which much larger propagation velocities were observed. The flame stretch effects (coupled with Le-effects) within a narrow space were suspected as the reason. The structural transition of the premixed flame could be investigated successfully through various disk-gaps, from the smallest quenching-scale to the ordinary large scales via whole mesoscales including Hele–Shaw scales.     

Laminar flame propagation of acetone and 2-butanone at normal to high pressures: Insight into fuel molecular structure effects of ketones

This work reports an experimental and kinetic modeling investigation on the laminar flame propagation of acetone and 2-butanone at normal to high pressures. The experiments were performed in a high-pressure constant-volume cylindrical combustion vessel at 1–10 atm, 423 K and equivalence ratios of 0.7–1.5. A kinetic model of acetone and 2-butanone combustion was developed from our recent pentanone model [Li et al., Proc. Combust. Inst. 38 (2021) 2135–2142] and validated against experimental data in this work and in literature. Together with our recently reported data of 3-pentanone, remarkable fuel molecular structure effects were observed in the laminar flame propagation of the three C₃C₅ ketones. The laminar burning velocity increases in the order of acetone, 2-butanone and 3-pentanone, while the pressure effects in laminar burning velocity reduces in the same order. Modeling analysis was performed to provide insight into the key pathways in flames of acetone and 2-butanone. The differences in radical pools are concluded to be responsible for the observed fuel molecular structure effects on laminar burning velocity. The favored formation of methyl in acetone flames inhibits its reactivity and leads to the slowest laminar flame propagation, while the easiest formation of ethyl in 3-pentanone flames results in the highest reactivity and fastest laminar flame propagation. Furthermore, the LBVs of acetone and 3-pentanone exhibit the strongest and weakest pressure effects respectively, which can be attributed to the influence of fuel molecular structures through two crucial pressure-dependent reactions CH₃ + H (+M) = CH₄ (+M) and C₂H₄ + H (+M) = C₂H₅ (+M).     

A dynamical system approach for solving the steady structure of high speed deflagrations

High-speed deflagrations have burning velocities much higher than laminar ones, and compressible effects become important. In the present paper, we study the structure of such high speed deflagrations in the thickened flame limit for a one-step Arrhenius rate law, whereby the transport coefficients are increased to give rise to buring velocities of finite Mach number. We study their steady structure and compare with the laminar low-Mach classical structure. The singular nature of both the fresh and burned gases conditions in the compressible regime, i.e., for large values of flame propagation Mach number, which are both saddle points, precludes the application of simple shooting methods to obtain their structure. The steps leading to the flame structure borrow techniques used to treat mathematical features commonly found in the study of dynamical systems (phase portrait of the flame structure equations system, eigenvalue decomposition of its linearized version), that can also be used to further comment on the nature of high-speed flames. The method proposed permits to determine the structure of deflagrations propagating up to speeds of aproximately 0.95 of the CJ-deflagration burning velocity, for a wide range of gas parameters commonly found in the field of numerical simulation of accelerating flames and their transitions to detonations. We comment on how the increasing role of compressibility modifies the structure of the laminar flame.     

Burning rates of turbulent iso-octane aerosol mixtures in spherical flame explosions

Experimental studies of aerosol combustion under quiescent and turbulence conditions have been conducted to quantify the differences in the flame structure and burning rates between aerosol and gaseous mixtures. Turbulence was generated by variable speed fans to yield rms turbulence velocities between 0.5 and 4.0 m/s and this was uniform and isotropic. Homogeneously distributed and near monodispersed iso-octane-air aerosol clouds were generated using a thermodynamic condensation method. Spherically expanding flames, following central ignition, at near atmospheric pressures were employed to quantify the flame structure and propagation rate. The effects of the diameter of fine fuel droplets on flame propagation were investigated. It is suggested that the inertia of fuel droplets is an important cause of flame enhancement during early flame development. During later stages, cellular flame instability and the effective, gaseous phase, equivalence ratio becomes important. The latter effect leads has increases the flame speed of rich mixtures, but decreases that of lean ones. Droplet enhancement of burning velocity can be significant at low turbulence but is negligible at high turbulence.     

Flame speed and self-similar propagation of expanding turbulent premixed flames

In this Letter we present turbulent flame speeds and their scaling from experimental measurements on constant-pressure, unity Lewis number expanding turbulent flames, propagating in nearly homogeneous isotropic turbulence in a dual-chamber, fan-stirred vessel. It is found that the normalized turbulent flame speed as a function of the average radius scales as a turbulent Reynolds number to the one-half power, where the average radius is the length scale and the thermal diffusivity is the transport property, thus showing self-similar propagation. Utilizing this dependence it is found that the turbulent flame speeds from the present expanding flames and those from the Bunsen geometry in the literature can be unified by a turbulent Reynolds number based on flame length scales using recent theoretical results obtained by spectral closure of the transformed G equation.     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.     

Laminar burning velocity and ignition delay time for premixed isooctane–air flames with syngas addition

The effects of blending syngas in different proportions to isooctane on the laminar burning velocity and ignition delay time of the fuel–air mixture have been studied in SI engine relevant conditions. The syngas is assumed to be composed of 50% H₂ and 50% CO. Simulations have been carried out using a skeletal mechanism containing 143 species and 643 reaction steps. It has been found that the blending of syngas augments the laminar burning velocity of isooctane due to increase of the thermal diffusivity of the reactant mixture and alteration in the chemistry of the flame reactions. For the mixture of 30% isooctane/70% syngas, the laminar burning velocity and the ignition delay time values are very close to those corresponding to pure isooctane. Additionally, the effects of exhaust gas recirculation have been explored for the 30% isooctane/70% syngas–air flame. It is seen that the reduction in laminar burning velocity due to the dilution by the recirculated exhaust gas can be compensated by an increase in the unburnt gas temperature. The effect of the exhaust gas dilution on the ignition delay time of 30% isooctane/70% syngas–air mixture has been found to be negligible.     

Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures

Laminar burning velocities of dimethyl ether (DME) and air premixed flames at elevated pressures up to 10 atm were measured by using a newly developed pressure-release type spherical bomb. The measurement system was validated using laminar burning velocities of methane–air flames. A comparison with the previous experimental data shows an excellent agreement and demonstrates the accuracy and reliability of the present experimental system. The measured flame speeds of DME–air flames were compared with the previous experimental data and the predictions using the full and reduced mechanisms. At atmospheric pressure, the measured laminar burning velocities of DME–air flames are in reasonable agreement with the previous data from spherical bomb method, but are much lower than both predictions and the experimental data of the PIV based counterflow flame measurements. The laminar burning velocities of DME–air flames at 2, 6, and 10 atm were also measured. It was found that flame speed decreases considerably with the increase of pressure. Moreover, the measured flame speeds are also lower than the predictions at high pressures. In addition, experiments showed that at high pressures the rich DME–air flames are strongly affected by the hydrodynamic and thermal-diffusive instabilities. Markstein lengths and the overall reaction order at different equivalence ratios were extracted from the flame speed data at elevated pressures. Sensitivity analysis showed that reactions involving methyl and formyl radicals play an important role in DME–air flame propagation and suggested that systematic modification of the reactions rates associated with methyl and formyl formations are necessary to reduce the discrepancies between predictions and measurements.     

Spatiotemporal measurements of flame stretch and propagation rates for lean and rich CH4/air premixed flames interacting with a turbulent-wake

A 1.5 m long turbulent-wake combustion vessel with a 0.15 m × 0.15 m cross-sectional area is proposed for spatiotemporal measurements of curvature, strain, dilatation and burning rates along a freely downward-propagating premixed flame interacting with a parallel row of staggered vortex pairs having both compression (negative) and extension (positive) strains simultaneously. The wanted wake is generated by rapidly withdrawing an electrically-controlled, horizontally-oriented sliding plate of 5 mm thickness for flame–wake interactions. Both rich and lean CH₄/air flames at the equivalence ratios  = 1.4 and  = 0.7 with nearly the same laminar burning velocity are studied, where flame–wake interactions and their time-dependent velocity fields are obtained by high-speed, high-resolution DPIV and laser-tomography. Correlations among curvature, strain, stretch, and dilatation rates along wrinkled flame fronts at different times are measured and thus their influences on front propagation rates can be analyzed. It is found that strain-related effects have significant influence on front propagation rates of rich CH₄/air (diffusionally stable) flames even when the curvature weights more in the total stretch than the strain rate does. The local propagation rates along the wrinkled flame front are more intense at negative strain rates corresponding to positive peak dilatation rates but the global propagation rate averaged along the rich flame front remains constant during all period of flame–wake interaction. For lean CH₄/air (diffusionally unstable) flames, the curvature becomes a dominant parameter influencing the structure and propagation of the wrinkled flame front, where both local and global propagation rates increase significantly with time, showing unsteady flame propagation. These experimental results suggest that the theory of laminar flame stretch can be applicable to a more complex flame–wake interaction involving unsteadiness and multitudinous interactions between vortices.